Parmenides as the Refutation of

Parmenides is the first philosopher to take explicit notice of contradiction. His realization is at the same time breathtakingly simple and fundamental. The power of his realization is easy to miss. The argument will proceed in five parts:

A.) A general account of contradiction, and its reation to truth.B.) How Parmenides uses contradiction in his philosophy.C.) What “the principle of contradiction” is.D.) Answers to some objections to the formulation given of the Principle of contradiction.E.) Parmenides’ response to the problems of skepticism.

Part A.) Contradiction is a species of contrariety. Contrary things are such that only one can be true, and in strict contraries, the truth of one will assure the falsity of the other; e.g. “I’m going to get either a tie or a shirt for our anniversary”. It is possible, however, for neither one of the contraries to be true, because whenever one is confronted with contraries they can never be certain if they have exhausted all the possibilities. Since both possibilities can be false, one can never be certain from a given set of contraries alone, that there is a truth to be discerned. Contradictories are more strict than this, and more powerful. In any set of contradictories, one is true, the other false; e.g. “I’m either going to get a tie for our anniversary, or I’m not”. Here we know that one of the options is true.

Contradictories, then, evince truth by their nature. Asking a question like “when do contradictories require truth?” is like asking “when do squares have four equal sides?” It can be helpful to look at the three possible answers that one might give to these questions.

1.) One could point out that the question was meaningless:squares and contradictories (hereafter, “s/c”) don’t lack the properties spoken of at one time, and then acquire them at another. To ask about “when” they pick up these properties is a meaningless question.

2.) One could say that the question should be answered “always”. We need to make a distinction, however, in this answer. S/c do not have the said properties always in the same sense that the earth is always spinning. In the case of the Earth, its spinning is a contingent fact- it is quite possible for it to stop doing so, which is to say that this could always happen in fact. The said properties of S/c use a stronger sense of “always”, it is not simply that they always are, but also that they cannot not be.

3.) One could say that the question should be answered “as soon as s/c exist”. In this response, we are making a distinction between the nature of the thing and whether the nature exists. At this point, we must divide the question about square from the question about contradictories. In the case of the square, we prove that it exists by actually making one- as happens, or example, in Elements 1.46. We do not prove that contradictories exist, or at least not in the same way. If one were to try to “prove” that a square exists by simply pointing to various examples of it, they would be guilty in the eyes of the geometer of begging the question, but pointing out or thinking about a few examples of contradiction is sufficient to show that contradiction exists. Even if, per impossibile, someone were to say “contradiction does not exist”, this denial would still require that the contradiction of contradiction (whatever that is) is necessarily the case. This argument is not question begging, as though we are assuming something that is hypothetically denied- it is rather to simply notice what the impossible premise means; for since the terms of the proposition are both used universally, the form of the impossible premise is either “Every ______ is not ______.” or “No _______ is _______” and the terms are convertable. It makes no difference how we choose to phrase it, for makes no difference to the truth of the matter whether we affirm the denial (is not) or deny the affirmation (is).

Contradiction, then, both is knownto be, and it requires that some known truth to be. The skeptic, however, has recourse to one last distinction that might save his skepticism, because even though for any set of contradictories there must be one option that is true, it does not follow from this that we are able to discern which of the opposites is the true one. It may be true enough that I must either get a tie for my anniversary or not- but how does this noting this get me ay closer to knowing which of the opposites will happen?

Part B.) The genius of Parmenides was that he did not speak about this or that particular contradiction, but rather that he spoke of contradiction as such. When he lays out what he calls “the path of persuation” he says that we know “that it is, and that it is not possible for it not to be” and that it is opposed to “the path of mortal opinion” which “is not…and it is necessary for it not to be”. Formally, then, these two ways are distinguished by contradiction, the one being wholly opposed to the other. But what sort of thing does the first way deal with? We note at this point that the two ways Parmenides lays out are not wholly distinguished by the sort of things they treat of: for he says that the way of mortal opinions will be taught because “the things that appear must genuinely be, being always, indeed, all things.” It seems then that Parmenides treats of “all things” in the path of persuation, not in the sense that he treats of a collection of particulars, but rather that he treats of all things as all, i.e. all things inasmuch as they are all “one, and continuous”. Parmenides thus avoids the last objection of the skeptic, for he is not speaking about this or that contradiction, but rather contradiction as it is manifest in the all taken as all.

As my last argument is not only controversial, but also the heart of my argument about how one should read Parmenides, I’ll sketch it out in detail:

1.) Parmenides desires to found a philosophy that is irrefutably true. He may do this because he is aware of the problem of skepticism, either from learning it from another, or by thinking it through for himself.

2.) Parmenides comes to understand that there is a peculiar power to contradiction- namely that by nature it requires the existence of a truth. This is to say that contradiction, taken generally, requires that we know something to be true, even though it does not require us to know the truth of this or that particular contradiction.

3.) Since Parmenides realizes that contradiction need not give us knowledge of a truth in any particular instance, he makes his philosophy treat of all things as all, as opposed to treating of any particular contradiction as such.

4.) Because he seeks to have a philosophy that treats of all things as all, but to give a name to this is to leave oneself open to the objection that they are really treating of some particular thing (like “being” or “whatever is” or “all corporeal things” etc..) Parmenides intentionally leaves the subject matter of his philosophy nameless. It makes no difference whether one describes the thing that Parmenides is speaking of as “being” or “whatever is, inasmuch as it is” or “all things as one” or “the cosmos taken as one thing” sapiens non curat de nominibus. What matters is that we see him as speaking about things on a general enough level to be to admit of contradiction generally, for contradiction in general requires the existence of some known truth.

Part C.) Again, even if we were ambivalent or skeptical about whether this or that being existed (say a man, a triangle, or even a cosmos), when we ascend to the level of being as such, we know that being is, and cannot not be. This statement, when taken as a principle (i.e. when taken as a thing from which something else proceeds), is called the principle of contradiction.

To call this the principle of contradiction may raise some hackles, as this principle “being is, and cannot not be” seems different from the more known formulation of the principle of contradiction, namely “Nothing can both be and not be at the same time and in the same respect”, but these two formulations of the principle amount to the same thing. The most apparent difference is that the second formulation includes “at the same time and in the same respect”. This addition, however, is not an addition that is necessary to the principle as such, but only for our first understanding of the principle. For if these additions were necessary to the principle as such, then it would follow that we necessarily knew that being as such was both temporal and distinguishable in different respects. We clearly do not know this, and even if we knew it, it would not be known from the nature of contradiction as such. In other words, it does not matter to contradiction as such, or the articulation of contradiction as such, whether being is temporal or distinguishable in different respects. It is quite possible for being to be atemporal, and absolutely one without distinguishable parts. We add this addition “in the same time and in the same respect” not because it is necessary for the truth of the principle, but rather because it is necessary for our first understanding of the principle, which will be grounded in an understanding of particular temporal things with distinguishable parts.

Said another way, to say “being cannot both be and not be, at the same time and in the same respect” is the same as saying “being cannot both be and not be, unqualifiedly“. But the very reason why we are speaking of “being” (or its contradictory, nothing) is that we desire to speak of things unqualifiedly, that is, not as any separate modality of what is, or as something divided from all things as one, but rather as they are known to us prior to any particular qualification. When one unerstads what is meant by “being is and cannot not be”, they see any addition made to it as superfluous and redundant to the principle itself.

All that remains of the more well known principle of contradiction is “Nothing can both be and not be”, but this is the same as saying (broken up for easier following)

a.) “what is not nothing cannot both be and not be”b.) but this is the same as saying “what is cannot both be and not be”c.) but since what is, obviously is, then the principle amounts to “what is, is, and cannot not be”d.) But “what is” is used as a synonym here for “being”.

and so the principle ends up as “being is, and cannot not be.”

Again, if one wanted to add to this principle “at the same time and in the same respect” we have no objection, we only ask that in this case they realize that they are adding to being the qualification of “being as temporal” and “being as distinguishable into parts”. We may allow this addition to make clear a particular instance of being which is more known to us; but the principle of contradiction, which is also known, transcends any particular instance of what is.

Even though we can cut the temporal and distinguishable qualification of being from the principle of contradiction, we are not able to go futher and reduce the principle to “being is”. The obvious reason for this is that to do so would be to loose contradiction as such, and it is though knowledge of contradiction that we come to know that we we must have knowledge of some truth. “Being is” is an affirmation, and an affirmation as such is not necessarily related to some truth, whereas cotradiction by nature is. It follows from this that our awareness of truth, of that thing that is and must be, is an awareness of what is, inasmuch as it is opposed to what is not and cannot be.

Part D.) If one were to say that this articulation of the principle could not be true, for any particular temporal being, say “Caesar” at one time was but at other time was not, we answer that Caesar is not the same as “being”. This or that being might pass away or come to be, but this or that being is not the same thing as being as such, and it is only on the level of being as such that the principle of contradiction yields a necessarily known truth- hence it is the only level at which Parmenides becomes interested. As it happens, Parmenides doesalso seem to think that the principle of contradiction proves that no particular being can either come to be or pass away, but we will deal with this particular argument in the next part of this essay.

While it is self evident that what is is, the skeptic might object to saying that the principle of contradiction requires that being cannot not be. Is it not possible that all being is contingent, and thus able to be to not be? We resolve this by noting that every contingent thing can in one sense become another, and in another sense cannot. For whatever becomes another must, by definition, be other than what it is- if this becomes that, then it must cease being this. This change either happens because something that is different from the thishas been added to it, or because something has been taken away (a tree becomes a bowling pin by ceasing to be a tree, while wood becomes a bowling pin by gaining a signification that was not present in wood as such). But “being as such” or “all things as one” does not admit of a difference, for nothing is different from being taken as such. Even if we were to note that “being” or “all things as one” have as their opposite the something called “nothing”, how could this “nothing” be added to what we start with? To add or take away “nothing” would be to change nothing. Those who would say that being as such could be changeable, therefore, are confounding the distinction between “being as such (or, being taken generally)” and “this or that particular being”. They are confouding “wha it is to be” with “this thing that is”, which makes no more sense than confonding “what a man is” with “this guy, say, Joe” Again, Parmenides himself may confound this distinction, but it makes no difference to the general truth of his philosophy, as will be dealt with in the next part. The particular problems with Parmenides’ philosophy do not affect his refutation of skepticism.

Part E.) Parmenides’ philosophy, when seen as pertaining to being as such, provides an absolute refutation of skepticism. For it the claim of skepticism that knowledge of the truth is denied in principle human beings; but the principle of contradiction, rightly understood, proves that truth must be knowable to human beings- since we know contradiction (i.e. contradiction as it is in being as such), and so we must also know truth as such, for contradiction cannot be known apart from truth, any more than “triangle” can be known apart from “three” or “side”.

We are now in possession of an account that can answer the particular claims of the skeptic. The skeptic, remember, said that belief goes over all things. But belief is the holding of something that can either be or not be. To hold such a thing, however, obviously requires a posterior awareness that “something can either be or not be” but this posterior awareness is founded on an awareness of contradiction, such that if contradiction were denied, then the very idea of belief must be denied, and if belief is affirmed, then contradiction must be affirmed as prior to it. Belief, then, far from being an alternative to truth as known, is actually founded on the truth given as known by contradiction.

There is also a fundamentl flaw in the skeptic’s understanding of the distiction between subject and object. The skeptic takes the distiction between subject and object as primary, such that this distinction divides two classes of being in a way that cannot be transcended. Any distiction or qualification of what is, or the all, however, presupposes some awareness the distiction between what is and what is not, which are manfest to human knowledge through the principle of contradiction. The skeptic makes something primary which simply is not primary- he posits a non-transcendable distinction that can only be posited if it has already been transcended. This is not to say that skeptics do not continually appeal to the principle of contradiction- quite the opposite. Experience shows that skeptics invoke contradiction continually, and (in fact) they can do no other. The fault, however, is that the skeptic’s understanding of the principle ofcontradiction is shallow and unreflective- and most often dismissive. The skeptic fails to appreciate the way in which the principle of contradiction establishes transcendental objectivity; for as far as the principle of contradiction is concerned, “subject” and “object” are one and undistinguished, since both are merely further determinations of all things as one, or all being, or the cosmos as one.And what of the skeptic’s claim that to seek knowledge is in some way impious to the gods? We may see Parmenides addressing this concern by presenting his philosophy itself as a revelation from a nameless goddess, but it ay be better to see him answering the skeptic’s claim in this fragment:

First of all gods, she contrived love

The quotation might strike the modern ear as sacarine and hallmark-ish, but when taken seriously, the fragment does a great deal of work. Love is, after all, a desire to share ones life with another- at least when it is between two intelligent beings. A universe that has love contrived above all things is not one where the gods would deny to human beings the goods that the gods enjoy. In this quotation, Parmenides provides a fuller, more positive account of why the gods would not deny wisdom to man than Aristotle does, when he argues against the claims of Simonides: